Lattice evidence for gauge field localization on a brane

We examine the problem of gauge-field localization in higher-dimensional ga uge theories. In particular, we study five-dimensional U(1) by lattice tech niques and we find that gauge fields can indeed be localized. Two models ar e considered. The first one has anisotropic couplings independent of each o ther and of the coordinates. It can be realized on a homogeneous but anisot ropic flat Euclidean space. The second model has couplings depending on the extra (transverse) fifth direction. This model can be realized by a U(1) g auge theory on the Randall-Sundrum background. In both models a new phase e xists, the layer phase, in which a massless photon is localized on the four -dimensional layers. We find that this phase is separated from the strong c oupling phase by a second order phase transition. (C) 2001 Published by Els evier Science B.V.